Texas Sen. Ted Cruz has leapfrogged from third to first place in the Republican presidential race in Iowa, a key early caucus state, jumping over erstwhile leader Donald Trump and Florida Sen. Marco Rubio in the latest poll, NBC News reported.

The Monmouth University poll shows Cruz with the support of 24 percent of likely caucus-goers, ahead of Trump (at 19 percent) and Rubio (at 17 percent.)

While support for Cruz has jumped by 14 points since October, Ben Carson—who led the same poll two months ago—has dropped 19 points. Carson is now at fourth place with 13 percent support.

Jeb Bush received just 6 percent support in the new survey, followed by Rand Paul (4 percent), Carly Fiorina (3 percent) and John Kasich (3 percent).

Cruz is banking on the support of Iowa's sizable evangelical population. Thirty percent of evangelical voters back him, versus 18 percent who back Trump, 16 percent who back Rubio and 15 percent who back Carson.

In October, Carson held the lead with the evangelical voting bloc, getting 36 percent support.

Cruz's sudden rise in popularity came after his camp released a tough-talking campaign ad on Saturday in which he promises to "kill the terrorists."

The ad, posted to YouTube and reported by The Hill, features the Texas senator up against a blurred background, promising that "America will lead" and "rebuild its military."

"We won't cower in the face of evil," Cruz says. "America will lead. We'll rebuild our military. We'll kill the terrorists. And every Islamic militant will know, if you wage jihad against us you're signing your death warrant."

The ad was released just days after the shooting rampage in San Bernardino, California, an act of terrorism perpetrated by a radicalised Muslim couple who killed 14 people.

On Monday, Cruz continued making waves, saying abortion could be "outlawed" in the U.S. through legislation, Raw Story reported.

Appearing on a Catholic talk show on EWTN, Cruz said he agrees with host Robert George that an interpretation of the 14th Amendment would seem to indicate that a foetus could receive protections under the Equal Protection Clause if granted that right by lawmakers.

"I think the first obligation of everyone in public office is to protect life. Life is foundational. In fact, as you look at the Declaration, that ordering of unalienable rights — life, liberty and the pursuit of happiness — I think is a very deliberate ordering," Cruz said.

"I very much agree with the pope's longstanding, and the prior popes' before him, longstanding call to protect every human life from the moment of conception to the moment of natural death," he pointed out.

"And we can do that by congressional action without waiting for the Supreme Court to overturn Roe v. Wade?" George asked.

"Absolutely yes, under the 14th Amendment," Cruz replied.